On mean values of some zeta-functions in the critical strip
Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 163-178.

Un entier k3 et un réel σ tel que 1 2<σ<1 étant fixés, on considère dans la formule asymptotique

1 T ζ(σ+it) 2k dt= n=1 d k 2 (n)n -2σ T+R(k,σ;T),
le terme erreur R(k,σ;T), pour lequel nous montrons de nouvelles bornes lorsque min (β k ,σ k * )<σ<1. Nous obtenons également des majorations nouvelles pour les termes erreur dans le développement des moments d’ordre deux des fonctions zêta de formes paraboliques holomorphes et des séries de Rankin-Selberg.

For a fixed integer k3, and fixed 1 2<σ<1 we consider

1 T ζ(σ+it) 2k dt= n=1 d k 2 (n)n -2σ T+R(k,σ;T),
where R(k,σ;T)=0(T)(T) is the error term in the above asymptotic formula. Hitherto the sharpest bounds for R(k,σ;T) are derived in the range min (β k ,σ k * )<σ<1. We also obtain new mean value results for the zeta-function of holomorphic cusp forms and the Rankin-Selberg series.

@article{JTNB_2003__15_1_163_0,
     author = {Ivi\'c, Aleksandar},
     title = {On mean values of some zeta-functions in the critical strip},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {163--178},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     zbl = {1050.11075},
     mrnumber = {2019009},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2003__15_1_163_0/}
}
Ivić, Aleksandar. On mean values of some zeta-functions in the critical strip. Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 163-178. http://www.numdam.org/item/JTNB_2003__15_1_163_0/

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